The application relates generally to surface analysis using electromagnetic radiation (also referred to herein as “light”) and particularly to rapid measurements for determining Stokes parameters which describe the polarization of radiation.
Ellipsometry is an extremely sensitive sample analysis technique which can be done non-destructively on most samples. During an ellipsometry experiment, light of one or more wavelengths is reflected from a surface of a sample, or transmitted through the sample and out the other side. Reflected light is more often analyzed and most of the discussion herein pertains to the analysis of reflected light in order to simplify the discussion. The information ellipsometry provides generally characterizes the surface of the sample near the reflection since the reflected light typically interacts less with the sample material away from the surface.
In order to appreciate the principles of ellipsometry, one can visualize the effects a surface may have on a linearly polarized light beam upon reflection. FIG. 1 is a schematic of the optical effects sustained by electromagnetic radiation (also referred to as light) during a reflection from a surface of a sample. FIG. 1 shows a linearly polarized light beam, polarized in a direction 100 composed of a polarization parallel to a plane of incidence 106 (also referred to as p-polarized light) and a polarization perpendicular to the plane of incidence 103 (s-polarized light). The figure shows the oscillations of the electric field at an instant in time. The distance for an oscillation to repeat is the wavelength 107. The light 109 propagates toward the sample 112 and reflects from the surface 113 of the sample 112. The angle of incidence 115 is measured from the surface normal 114 (a line mentally drawn which is perpendicular to the plane of the surface 113).
During the reflection, the light undergoes changes in phases and amplitudes as a result of the interaction with the sample surface. The p-polarized light may sustain a different change-in-phase than the s-polarized light. Similarly, the electric field amplitude of p-polarized (s-polarized) light before reflection may be different from the electric field amplitude of p-polarized (s-polarized) light after reflection. Furthermore, the change in electric field amplitude of p-polarized light before and after reflection may not be the same as the change in electric field amplitude of s-polarized light before and after reflection. Moreover, the ratio of the electric field amplitudes of p-polarized light after and before reflection may not even be the same as the corresponding ratio for s-polarized light. These changes may have different characteristics for a different choice of wavelength 107.
Following a reflection, light propagates away from the sample 118 with the same wavelength but perhaps new amplitudes and phases. The line of propagation after reflection and the line of propagation before reflection occupy a “plane of incidence” as used herein. After reflection, the s-polarized light 124 and the p-polarized light 127 may no longer be coherent. Rather, the oscillations of the s-polarized light 124 and the p-polarized light 127 are separated by a phase angle 130. A non-zero phase angle 130 results in an electric field (interchangeably referred to as the polarization 121) which may not always point in the same direction as the light propagates. The polarization 121 rotates. Once again, the light is depicted at an instant in time to show these details. The polarization 121 also rotates when viewed by a stationary observer. As the light passes a plane 133 the direction of the polarization (the combination of the s-polarized and p-polarized light) rotates counter-clockwise in the schematic illustration. Note that the magnitude is not constant as the elliptical path 134 indicated by arrows is traced.
The polarization of the reflected light is normally determined by characterizing the circumscribed ellipse 134 of FIG. 1. Characterizing the ellipse 134 is one of the steps of ellipsometry and the measurement can be made using a small number of optical elements. Four parameters known as Stokes parameters are often used to describe an optical polarization. The four Stokes parameters (S0, S1, S2 and S3) can be thought of as specifying the size of a Poincaré sphere and a location on the surface of or within the Poincaré sphere. A location within the Poincaré sphere indicates partially polarized light. S0 represents the size of the sphere and the remainder of the parameters represent the location of a point. Roughly speaking, S3 is indicative of how close the ellipse 134 is to a circle and S1, S2 are indicative of the orientation of the ellipse 134 in FIG. 1 as well as whether the polarization 121 rotates clockwise or counter-clockwise.
There are multiple physical arrangements in use for acquiring data which allow the determination of some or all of the Stokes parameters. Measurements which acquire all the Stokes parameters are preferable. Most ellipsometry measurements are made with setups arranged as in FIG. 2. Light 203 originates from a light source 200 and travels toward a polarizer 206 (the polarizer 206 may be represented by the letter “P” herein). Polarized light 207 exits the polarizer 206 and reflects from the surface 212 of a sample 209 (represented by an “S”). The reflected light 213 continues toward a wave plate 221 (represented by a “W”). P-polarized light and s-polarized light travel at different speeds within the wave plate 221 and the thickness is often chosen to impart a quarter wavelength difference in phase between p- and s-polarized light. Such a wave plate 221 is called a quarter wave plate. After emerging from the wave plate 221, the light proceeds toward an analyzer 233 (represented by an “A”). The analyzer may be a polarizer which allows a linearly polarized light beam through to the detector 260. The sequence of objects can be represented succinctly as PSWA.
In these prior art systems, one of the elements may rotate in order to make a measurement of some or all of the Stokes parameters. A subscript “R” may be added to an optical element rotated during a measurement. Table I correlates object sequences with the Stokes parameters which can be determined. The results shown in Table I assume objects without the subscript “R” are stationary during the measurement(s). The position of the sample can be changed from before the wave plate to after the wave plate in PSWAR and PSWRA without impacting the list of measurable Stokes parameters.
TABLE IPhysical Arrangement of Prior Art EllipsometersMeasurable StokesObject SequenceParametersPSARS0, S1, S2PSWARS0, S1, S2PSWRAS0, S1, S2, S3
The PSWRA configuration, with a rotating wave plate, enables the determination of four Stokes parameters. Though the four Stokes parameters can be determined, a remaining problem is the speed with which a measurement can be made.
A reliance on rotating or moving optical elements (such as a wave plate) to make a measurement, delays the acquisition of the data needed to determine the Stokes parameters. Besides a reduced throughput, requiring motion of optical requirements introduces significant reliability issues and increases the complexity of data acquisition due, in part, to timing issues.